You need to create transports to move troops between planets and if I remember correctly each transport = 4 troops. Things you need to consider if you want to win are: superior numbers and/or more advanced troops. Advanced techs make your men better rapemachines, so you'll need less troops to conquer more primitive empires. Superior numbers are the only that'll save you if you're fighting an equal enemy. Land battles resolve automatically, and the outcome is random generated (bonuses highly modify it though, in your, or your enemies favour depending on who's more advanced), so even despite your Warlord and Grav Harness and Uber Layzors you might somehow lose.
Space battles are pretty much space chess with pawns shooting at each other with various stuff. First one to lose hull strength explodes, so make sure you've got better guns, or/and bigger numbers. You control your units, there are separate forward/sides/back shields, through which layzors must get through to damage the ship. Some weapons get through shields, but they do less damage, some weapons do little damage to shields, but they eradicate armour, some can't pass through armour, but they own hull etc. You may also capture ships by sending marines if those ships are at point-blank distance, or via assault shuttles on a bigger distance, but those shuttles may be shot down. Ships range from tiny scouts with a single laser to motherfucker death star-alike constructions with stellar converters, weapons that destroy planets. All ships are fully modular, so you configure what stuff's inside. Except for weapons, there are also gimmicks that allow for, for instance, make the hull stronger, store more marines on-board, install systems that destroy missles coming at your ship or making your missles more successful at scoring hits etc. Dunno what to say more.